Question: Compute probabilities for the following compound events:
Mr. Andrews, a grape merchant, inquires about a certain wine that he tastes at a party. The host tells him that from a total of ten bottles of that wine, six came from the north vineyard and four came from the south vineyard. From this information, the merchant concludes that he should visit the north vineyard for a sample of the grapes. Later, he discovers that the wine in question came from a bottle labeled Classic Reserve, and 30 of 100 barrels of north vineyard wine were bottled with that label, while 130 of 200 barrels of south vineyard wine were bottled with that label. Given this new information, what is the probability that the wine came from the north vineyard?